Average Error: 3.1 → 0.1
Time: 27.5s
Precision: 64
Internal Precision: 576
\[1 - \frac{1}{a} \cdot {\left(1 - b\right)}^{\left(\frac{3}{2}\right)}\]
\[1 - \frac{{\left(1 - b\right)}^{\left(\frac{1}{2} \cdot \frac{3}{2}\right)}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}\]

Error

Bits error versus a

Bits error versus b

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 3.1

    \[1 - \frac{1}{a} \cdot {\left(1 - b\right)}^{\left(\frac{3}{2}\right)}\]
  2. Applied simplify3.1

    \[\leadsto \color{blue}{1 - \frac{{\left(1 - b\right)}^{\left(\frac{3}{2}\right)}}{a}}\]
  3. Using strategy rm
  4. Applied add-sqr-sqrt3.2

    \[\leadsto 1 - \frac{{\color{blue}{\left(\sqrt{1 - b} \cdot \sqrt{1 - b}\right)}}^{\left(\frac{3}{2}\right)}}{a}\]
  5. Applied unpow-prod-down3.2

    \[\leadsto 1 - \frac{\color{blue}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)} \cdot {\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}{a}\]
  6. Applied associate-/l*0.2

    \[\leadsto 1 - \color{blue}{\frac{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}}\]
  7. Using strategy rm
  8. Applied pow1/20.2

    \[\leadsto 1 - \frac{{\color{blue}{\left({\left(1 - b\right)}^{\frac{1}{2}}\right)}}^{\left(\frac{3}{2}\right)}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}\]
  9. Applied pow-pow0.1

    \[\leadsto 1 - \frac{\color{blue}{{\left(1 - b\right)}^{\left(\frac{1}{2} \cdot \frac{3}{2}\right)}}}{\frac{a}{{\left(\sqrt{1 - b}\right)}^{\left(\frac{3}{2}\right)}}}\]

Runtime

Time bar (total: 27.5s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (a b)
  :name "(1 - 1/a*(1 - b)^(3/2))"
  (- 1 (* (/ 1 a) (pow (- 1 b) (/ 3 2)))))